System and method for quantum cache

ABSTRACT

An entangled quantum cache includes a quantum store that receives a plurality of quantum states and is configured to store and order the plurality of quantum states and to provide select ones of the stored and ordered plurality of quantum states to a quantum data output at a first desired time. A fidelity system is configured to determine a fidelity of at least some of the plurality of quantum states. A classical store is coupled to the fidelity system and configured to store classical data comprising the determined fidelity information and an index that associates particular ones of classical data with particular ones of the plurality of quantum states and to supply at least some of the classical data to a classical data output at a second desired time. A processor is connected to the classical store and determines the first time based on the index.

The section headings used herein are for organizational purposes onlyand should not be construed as limiting the subject matter described inthe present application in any way.

RELATED APPLICATION SECTION

The present application is a non-provisional application of U.S.Provisional Patent Application Ser. No. 63/020,221 filed May 5, 2020 andentitled “System and Method for Quantum Cache” and a non-provisionalapplication of U.S. Provisional Patent Application Ser. No. 63/183,023filed May 2, 2021 and entitled “System and Method for Quantum Cache”.The entire content of U.S. Provisional Patent Application Ser. Nos.63/020,221 and 63/183,023 and are herein incorporated by reference.

INTRODUCTION

Information systems today are highly distributed, and this trend isexpected to continue especially as the next generation wireless systemskeep people and machines connected anywhere and anytime. Applicationsand services increasingly rely on distributed information and processingto function, yet also increasingly aim to operate, look and feel likelocal systems. These kinds of future systems can benefit from improvedmethods of tagging, storing, and moving information, including systemsthat utilize so-called non-local operations and resources. For example,methods and systems that can provide precise location and timinginformation that is not dependent on a communication channel, orsensitive to time-of-flight delay of those channels, are highlydesirable.

In addition, with so much information, including highly personal,confidential, and sensitive information, being an integral part of theapplications and services on which people and machines rely upon,improved methods of tagging, storing and moving that informationsecurely are also highly desirable. For example, methods of addressingthat are not dependent on sending a plain text address on acommunication link are desirable. In many cases, traditional classicalsystems have reached their technical limits on providing features tosolve these critical problems. Quantum solutions can offer manyimportant improvements. However, practical quantum systems are notcurrently available that fit seamlessly and effectively within classicalinformation systems such that the underlying quantum phenomena can beused to improve performance.

BRIEF DESCRIPTION OF THE DRAWINGS

The present teaching, in accordance with preferred and exemplaryembodiments, together with further advantages thereof, is moreparticularly described in the following detailed description, taken inconjunction with the accompanying drawings. The skilled person in theart will understand that the drawings, described below, are forillustration purposes only. The drawings are not necessarily to scale,emphasis instead generally being placed upon illustrating principles ofthe teaching. The drawings are not intended to limit the scope of theApplicant's teaching in any way.

FIG. 1 illustrates a distributed system that can utilize a quantumentangled cache according to the present teaching.

FIG. 2 illustrates an embodiment of a portion of the distributed systemdescribed in connection with FIG. 1 that includes nodes using a quantumentangled cache and a node using an entanglement server according to thepresent teaching.

FIG. 3 illustrates a block diagram of an embodiment of a quantumentangled cache according to the present teaching.

FIG. 4 illustrates an embodiment of a table showing a cache structurefor a quantum entangled cache according to the present teaching.

FIG. 5A illustrates a diagram of an embodiment of a multilayer quantumstore according to the present teaching.

FIG. 5B illustrates a table showing a cache structure for a multi-layerquantum entangled cache according to the present teaching.

FIG. 6A illustrates an embodiment of a bus network using an entangledcache according to the present teaching.

FIG. 6B illustrates a table showing an embodiment of a structure of anentangled qubit cache for a multi-node network according to the presentteaching.

FIG. 7 illustrates a block diagram of an embodiment of a quantum-enabledinformation system that uses an entangled quantum cache according to thepresent teaching.

FIG. 8 illustrates a block diagram of an embodiment of a control systemthat controls an entangled quantum cache interacting with an applicationaccording to the present teaching.

FIG. 9 illustrates an embodiment of a distributed system using anentangled cache to provide metadata according to the present teaching.

FIG. 10 illustrates a known quantum super dense coding schemeapplication operating between a transmitter and receiver.

FIG. 11 illustrates an embodiment of a super-dense coding system usingan entangled cache according to the present teaching.

FIG. 12 illustrates another embodiment of a super-dense coding systemusing an entangled cache according to the present teaching.

DESCRIPTION OF VARIOUS EMBODIMENTS

The present teaching will now be described in more detail with referenceto exemplary embodiments thereof as shown in the accompanying drawings.While the present teachings are described in conjunction with variousembodiments and examples, it is not intended that the present teachingsbe limited to such embodiments. On the contrary, the present teachingsencompass various alternatives, modifications and equivalents, as willbe appreciated by those of skill in the art. Those of ordinary skill inthe art having access to the teaching herein will recognize additionalimplementations, modifications, and embodiments, as well as other fieldsof use, which are within the scope of the present disclosure asdescribed herein.

Reference in the specification to “one embodiment” or “an embodiment”means that a particular feature, structure, or characteristic describedin connection with the embodiment is included in at least one embodimentof the teaching. The appearances of the phrase “in one embodiment” invarious places in the specification are not necessarily all referring tothe same embodiment.

It should be understood that the individual steps of the methods of thepresent teachings can be performed in any order and/or simultaneously aslong as the teaching remains operable. Furthermore, it should beunderstood that the apparatus and methods of the present teachings caninclude any number or all of the described embodiments as long as theteaching remains operable.

The present teaching relates to integrating quantum systems intotraditional classical information systems to form various quantuminformation systems. These quantum information systems rely on theirfundamental properties of quantization, superposition, entanglementand/or non-locality to provide various performance advantages and newfeatures over similar classical versions of information systemtechnologies. Some known examples of quantum information systems includequantum key distribution systems, analog and digital quantum computers,quantum communication links, and quantum sensors.

A particularly useful quantum object is the quantum qubit, which is asuperposition state of two basis states, which can generally bedescribed in Dirac notation as |0

and |1

. Different physical manifestations of qubits, for examplesuperconducting qubits, optical qubits, and atomic qubits, possessdifferent physical manifestations for these basis states. However, thesedifferent manifestations can be expressed with similar mathematicalrepresentations and they behave in a similar way in a quantum system. Itshould be understood that the present teaching can apply numerousmanifestations of quantum qubit systems.

The qubit coherent superposition of the basis states can be representedas |ψ

=α|0

+β|1

, where α and β are complex numbers that represent a probabilityamplitude for each of the basis states that is governed by a Schrodingerequation, which describes how the state evolves in time based on itsenergy environment. The probability distribution, which is the magnitudesquared of the probability amplitudes, indicates a probability a |0

or a |1

will result from a measurement of the qubit.

It is now widely accepted in the art that qubits can be entangled, whichallows that future measurements of particular ones of their physicalproperties be perfectly correlated with the other qubits with which theyare entangled. This feature of qubit entanglement is true even if theentangled qubits are separated in time and/or space. This is due, atleast in part, to the quantized nature of the entangled quantum system,and the fact that the wave function that describes the quantumprobability of the various superposed states of the system collapses toa single quantized state upon measurement.

Another feature of qubit entanglement is that measurement, as defined bythe quantum theory, affects the entangled system as a whole, leading toa phenomenon in which a measurement at one location causes an outcome,in the form of a collapsed state (commonly referred to as a wavefunction collapse) that is perfectly correlated with the measured state,at another location. This wave function collapse, and the associatedperfectly correlated outcomes at two locations, makes entangled qubitsand, more generally, entangled distributed quantum systems, particularlyuseful resources in numerous types of information systems.

It should be understood that observing a quantum state is notnecessarily a measurement of the quantum state. A measurement is anaction that collapses the state of the wave function that describes theentangled system. Physicists will often define a measurement as anaction that probes a path, or distinguishes with certainty, one of thepossible states of the entangled system. Once discovered throughmeasurement, a state of a quantum system is no longer in superposition,and no longer capable of maintaining a long-term correlation across itsdistributed system. Rather, the system irreversibly gives up this typeof connection.

Various aspects of the present teaching take advantage of the fact thatquantum systems provide an ability to establish a fidelity ofentanglement separately from a measurement. In general, the fidelity ofentanglement is a metric used to compare quantum states. The concept offidelity of entanglement is straightforward in the case of pure states,but is subtler for the mixed quantum states found in real system. Inother words, a quantum measurement is separable from other observationsof the quantum state that allow one to determine if the state is stillentangled. In fact, numerous methods are available to probe a quantumstate for entanglement without disturbing the entanglement causingcollapse of quantum states to occur where the system will then no longerbe entangled.

Many quantum systems according to the present teaching take advantage ofthe fact that the quantum aspect of the system can be prepared withentangled states and distributed, physically or virtually, acrossvarious physical locations. These entangled states can be measured toprovide perfectly correlated states to be determined at remotelocations. One feature of these systems is that no physical channel isnecessary to provide this correlated state determination. In variousembodiments, the quantum-entangled systems of the present teaching areseparated in space and/or time. Thus, various aspects of the presentteaching advantageously utilize of the fact that the state collapse thatprovides a correlated state determination at two locations occurs bothinstantaneously and without regard to a distance between thoselocations, and/or any aspect of a precise position of those locations.

Furthermore, various aspects of the present teaching advantageouslyutilize the fact that any external influences, such as an eavesdropper,that make a measurement of the quantum system, will destroy theassociated entanglement, causing a state collapse. Such a state collapsecan be positively determined through various known mechanisms andprotocols. Any observed or otherwise tampered quantum bit, or quantumsubsystem, which relies on a quantum state, can then be discarded ordisregarded as it no longer contains useful information. Thus, anotheraspect of the present teaching is that information systems according tothe present teaching can operate securely, and/or ensure privacy fromeavesdroppers or various outside influences for any outcome ormeasurement.

Another feature of the present teaching is the realization that hybridquantum/classical systems can still continue to operate over variousclassical channels, and/or use classical connections to manage theinformation they process, store and communicate. As such, variousembodiments of systems and methods of the present teaching stillmaintain data in a classical regime, and rely on any outcome ormeasurement associated with various ones of entangled qubits asclassical metadata, rather than the quantum state itself.

Another feature of the present teaching is the recognition thatmanagement mechanisms are needed, or at least highly desirable, tocontrol and manage the distribution and storage of quantum states.Quantum states can be transferred and stored using any of numerousmechanisms depending on the particular application and the method ofgenerating the quantum state. The mechanisms used to control and managethe quantum physical systems that generate the quantum states mustrecognize the key performance attributes of the physical qubits combinedwith the needs of the systems that are using the quantum state forvarious applications. Said another way, one feature of the presentteaching is providing various methods and apparatus for providingappropriate abstraction(s) that operate between the quantum physicalsystems that supply quantum states, and the classical, semi-classical,and/or quantum information systems that use that quantum states forvarious applications. The abstraction(s) make it possible for systemdesigner who are not skilled in the art of quantum systems but, areskilled in the art of classical system to include quantum systems aspart of designing solutions, thus providing a relatively simpleinterface bridge between quantum and classical systems.

Numerous important quantum applications utilize entangled qubitsdistributed in a network. The term “network” as used herein is a verybroad term that relates to a collection of two or more node associatedwith information. FIG. 1 illustrates an embodiment of a distributedsystem 100 that utilizes a quantum entangled cache according to thepresent teaching. A plurality of nodes 102 are connected by links 104.In general, the nodes 102 include both quantum systems and classicalsystems. Also, in general, the links can include classical transport orconnections, can also include quantum transport or connections, and canalso include links that can transport and/or connect both quantum andclassical data as described herein. The distributed system 100 is a meshtopology with nodes 102, 102′ and links 104. However, it should beunderstood that the present teaching can be applied to numerousdifferent and hybrid topologies. For example, the present teaching canbe applied to bus, star, tree, ring, point-to-point, hybrid and othernetwork topologies.

In some embodiments of the distributed system 100, entangled pairs, ormore generally, larger groupings of N-entangled qubits, such as three,four, or more entangled qubits in a group, are needed to be available inany number of entangled dimensions, K, when needed. In other words, thedistributed quantum entanglement cache of the present teaching caninclude a source of entangled quantum states that generates quantumstates having a plurality of entangled quantum states. Thus, qubits canbe shared with N nodes and include K basis states. The qubits areentangled and coherent to some degree when used in a node 102, 102′.Thus, for some configurations, a mechanism is used in the nodes 102,102′ to ensure coherent qubits, and to discard qubits that are notcoherent.

In some embodiments of systems according to the present teaching, amechanism is used in the nodes 102, 102′ or elsewhere to supply verifiedcoherent qubits. Also, in some embodiments of systems according to thepresent teaching, a mechanism is used to ensure a supply of qubits thatexceeds a predetermined percentage of coherent qubits out of a pool ofqubits available in the node.

In addition, it is important that the qubits be indexed so that pairingsare maintained between qubits in one node 102 compared with another node102′. Some embodiments of quantum distributed systems 102 according tothe present teaching have mechanisms to ensure that qubits are accessedwith a latency that is compatible with the particular application. Forexample, a mechanism can be used to appropriately synchronize theavailability of sets of from 2-N entangled qubits between 2-N nodes 102,102′ to ensure desired access latency and support the pairing of thosequbits. The indexing in the nodes 102, 102′ allows various pairings, orN-way entangled quantum states, to be identified with each other. Thatis, an index can be used to indicate which other node(s)' quantum statesa particular quantum state is entangled with.

The embodiment of the distributed system 100 in the descriptionassociated with FIG. 1, as well as other embodiments described herein,describe the use of caches that include entangled quantum states.However, it should be understood that caches of the present teaching arenot limited to entangled quantum states. As described herein,embodiments of quantum stores and quantum caches can include and utilizequantum states that are not entangled states and/or quantum states thatare entangled quantum states.

FIG. 2 illustrates an embodiment of a portion of the distributed system200 of FIG. 1 with a node 202 that performs as an entanglement serverusing an entanglement generator 204 and nodes 206, 206′ using a quantumentangled cache 208, 208′ according to the present teaching. The node202 is connected by links 210, 210′. Numerous embodiments of the presentteaching use a centralized and/or distributed mechanism for distributingentangled qubits.

Entangled qubits are supplied by entanglement generators 204. Thedistributed system 200 shown in FIG. 2 illustrates only two nodes 206,206′ that receive entangled qubits, and a node 202 connected to twolinks 210, 210′ that provides entangled quantum resources on those links210, 210′ for clarity. Distributed systems 200 according to the presentteaching are not so limited. For example, many nodes can receiveentangled resources. The entangled resource generator 204 can generateentanglement across more than two qubits, and so can be provided acrossmore than two links 210, 210′. Nodes 202, 206, 206′ can include eitheror both of server node resources 204 and cache resources 208, 208′.Also, multiple entangled qubit generators 204 can connect differentand/or the same caches 208, 208′. It should be understood that a diversearray of quantum and classical network connections can be realized usingthe present teachings.

One feature of the present teaching is the recognition thatdeterministic and on-demand sources of entangled photons can easily beintegrated into systems using classical indexing corresponding toparticular quantum states as well as other information associated withthe quantum state generation. Ideal deterministic sources produceentangled photons at known times and with 100% fidelity. In practice,deterministic sources approach these goals with a known and/orcharacterizable high probability (and/or fidelity) that a pair, or set,of entangled photons is produced at a known time. While these terms areoften used interchangeable, for purposes herein, on-demand sourcesproduce entangled photons at arbitrary but controllable times whiledeterministic sources produce entangled photons at known, predetermined,times with high probability. Importantly, both of these types ofcontrollable emission quantum entangled photon sources are amenable toattaching associated classical data, including indexing information andquantum integrity information. Associated classical data can be referredto as meta data.

Some embodiments of the entanglement server 204 use a deterministicsource of entangled photons that is generated by multiplexing and/orswitching of non-deterministic quantum photon sources. Many knownhigh-brightness sources of entangled photons are so-callednon-deterministic sources that produce entangled photon pairs (andlarger entangled sets), but at random times. For example, spontaneousparametric down conversion (SPDC), four wave mixing, and various othernonlinear parametric processes are known to provide entangled photonswith a high rate, though with non-deterministic emission times. Multiplesystems and methods have been shown to provide deterministic photonsources using multiplexing and/or switching schemes combined withnon-deterministic sources. See, for example, Evan Meyer-Scott, ChristineSilberhorn, and Alan Migdall, “Single-photon sources: Approaching theideal through multiplexing”, Review of Scientific Instruments 91, 041101(2020), which is incorporated herein by reference. As one example, aquasi-deterministic source can generally provide photon pairs and photonclusters (>2 entangled photons) substantially more than 60% of the timein a given time slot, with 99% fidelity. See, for example, Jeffrey H.Shapiro and Franco N. Wong, “On-demand single-photon generation using amodular array of parametric downconverters with electro-opticpolarization controls,” Opt. Lett. 32, 2698-2700 (2007), which isincorporated herein by reference. With such sources, it is possible toprovide a time window, including a repetitive time window for which anentangled photon pair will be provided at a particular position in thesystem, and it is also possible to specify that only 1% of the timewindows would have faulty quantum states (e.g. more than one photon).

Some embodiments of the entanglement server 204 use a deterministicsource of entangled photons that is generated by known, predeterminedloading or setting of quantum emitting states in the source. Forexample, various configurations of quantum dot sources can be used. See,for example, Hui Wang, Hai Hu, T.-H. Chung, Jian Qin, Xiaoxia Yang,J.-P. Li, R.-Z. Liu, H.-S. Zhong, Y.-M. He, Xing Ding, Y.-H. Deng, QingDai, Y.-H. Huo, Sven Höfling, Chao-Yang Lu, and Jian-Wei Pan, “On-DemandSemiconductor Source of Entangled Photons Which Simultaneously Has HighFidelity, Efficiency, and Indistinguishability,” Phys. Rev. Lett. 122,113602, (2019), which is incorporated herein by reference. Also see, forexample, Müller, M., Bounouar, S., Jöns, K. et al., “On-demandgeneration of indistinguishable polarization-entangled photon pairs,”Nature Photon 8, 224-228 (2014), which is incorporated herein byreference. Advantageously, the ability to index the expected arrivalslot or position of the entangled photon events can be provided forthese kinds of sources. In addition, it is possible to provideassociated classical data regarding, for example, the number ofindistinguishable events (e.g. identical photon states) that will followa prepared excitation state, the expected fidelity (dephasing, addedbackground) and other associated classical information about theentangled photons that allow these sources to be generally described andincorporated as part of a larger system as described herein. Theclassical information can be tagged to an individual entangled photonevent or a larger set of events, depending on the source. One feature ofthe present teaching is that the classical tagging process allowsmultiple types of sources to be used in the same system.

In some embodiments, the entanglement generator 204 can transmitgenerated entangled qubits using links 210, 210′ to the nodes 206, 206′.These transmitted qubits may be sent in quantum channels that areembedded in, or separate from, any classical channel(s) that is used forthe links 210, 210′ using various systems and methods for transmittingentangled qubits. The entanglement generator 204 can be electronic andcan generate entangled electronic qubits that are transmittedelectronically. The entanglement generator 204 can also be optical. Forexample, the entanglement generator 204 can be an entangled photonsource that generates entangled photons. These photons are sent overlinks 210, 210′ that include optical fiber that transmits the entangledphotons. These links could also be free space. Nodes 206, 206′ include aquantum entangled cache 208, 208′ for storing and retrieving entangledqubits at each node 206, 206′. Practical systems will appropriatelybalance the speed at which entangled bits are generated and consumed fora particular coherence half-life of the entanglement.

The quantum entangled caches 208, 208′ can include a mechanism fordetermining the coherence of qubits at each node. Coherence is a metricof the degree of entanglement. In some embodiments, this mechanismincludes a coherence detector with some discard mechanism. In someparticular embodiments, this mechanism has knowledge of reliablestatistics on coherence half-life and uses at least one of manydifferent types of error correcting coding. Qubits may be discardedafter an age-out, for example after a known half-life, or alternativelyan age-out based on a known error rate or error condition. In someembodiments, both these mechanisms are used. Some embodiments rely onentanglement purification, which uses measurements on a number, n, ofadjacent qubits to determine with high probability that a given qubit isentangled. Thus, various mechanisms can be used to determine coherenceof one or more qubits that are part of an entangled system.

The quantum entangled caches 208, 208′ also include a synchronizationmechanism that ensures matched pairs or sets of qubits are in use at thevarious nodes 206, 206′. The synchronization may, for example, beassociated with a particular known order of qubits in the cache that isassociated with, or registered to, another order of qubits in anothernode. In some embodiments, the synchronization mechanism is an orderedcache. In some embodiments, the synchronization mechanism uses classicalchannel information exchange. For example, the order of qubits in twodifferent nodes can be exchanged and updated as the order changes. Also,in some embodiments, the nodes are connected via a communication channel212 that can support one or both of quantum and classicalcommunications. This channel 212 may be the same or different from thelinks 210, 210′ that transmit photons to the caches 208, 208′.

FIG. 3 illustrates a block diagram of an embodiment of a quantumentangled cache according to the present teaching. Qubits are suppliedto a qubit loader 302 from a quantum channel 304 and/or a combinedquantum-classical channel 306. The supplied qubits are entered into aqubit store 308, which is a quantum store. The qubit store 308 is aphysical storage system that holds and maintains, to a predeterminedacceptable degree, the entanglement and coherence of ordered qubits.Thus, the qubit store 308 generally accepts qubit state from the loader302 into a physical mechanism that can maintain the coherence andentanglement of the qubit in an ordered way, such that an unloader 310can access and supply that state to an application 312. The qubit store308 is shown in FIG. 3 as a first-in-first-out (FIFO) structure suchthat the youngest qubit (to the cache) sits at the bottom slot 314 andthe oldest qubit sits at the top slot 316 of the qubit store 308 so thatthe oldest qubit would be next available to supply for an application312. It should be understood that the terms “top” and “bottom” arerelative terms used to describe the present teaching, but may or may notbe representative of a practical qubit storage system. For example, oneskilled in the art will appreciate that qubit store 308 could beimplemented in numerous ways such as with a simple fiber delay line,where a photonic qubit enters the delay line and would be the first toexit the delay line to be used by an application connected to the store.In various embodiments, the qubit loader 302 and/or the qubit unloader310 can comprise, for example, a passive coupler/splitter, a quantumswitch, an optical switch, a quantum wavelength converter, a quantumrepeater, and/or a quantum state converter.

Multiple types of storage systems are contemplated by the presentteaching. Various embodiments of the qubit store 308 can have variousphysical implementations and operation. This includes, for example fiberloops, including hierarchical fiber loops, which can achieve a varietyof input-output relationships between loaded photonic qubits andunloaded photonic qubits. For example, FIFO, last-in-first-out (LIFO),or other interleaved access architecture can be realized. In addition,numerous types of memory devices, such as those based on ions or atoms,are suitable for use as random access memory devices, as slots can beassociated with positions on, for example, a lattice or other orderedphysical arrangement that supports the particular quantum system. Forexample, slots might be associated with positions of nitrogen vacanciesin a diamond lattice. Thus, quantum entangled caches of the presentteaching are compatible with a variety of storage structures includingrandom access storage structures and stack-type storage structures, suchas FIFO and LIFO.

A classical data loader 318 takes in data from a classical channel 320and/or optionally a combined classical-quantum channel 306. Theclassical data loader 318 loads the data that is associated withparticular qubits into a classical store 322 that holds and maintainsthe classical data associated with particular qubits. The classicalstore 322 is conventional computer memory that can be volatile ornon-volatile memory that can take numerous forms that are well known inthe computer hardware art. A data unloader 324 can provide the classicaldata associated with a particular qubit to an application 325 such thatthe application is then able to use any subsequent information about thestate of the qubit effectively in the application. Subsequentinformation includes, for example, information obtained by processingthe qubit in a quantum logic element, making state-collapse inducing(non-unitary) measurement operations on the qubit, and/or makingmeasurements on the qubit that do not collapse the qubit state, butrather provide information about the state of the qubit or other qubitproperties. Thus, one aspect of systems and method of the presentteaching is that the quantum entangled cache 300 holds and maintainsclassical data associated with a qubit and provides that data to ahigher-layer application to aide in the application processing of thequbit.

The quantum entangled cache 300 includes a fidelity system 326 that isconnected to the quantum store 308 and to the classical store 322. Thefidelity system 326 can identify and remove or otherwise reject badqubits, such as a bad qubit in slot 327. This would include, forexample, qubits that have or will soon collapse and/or have lost certainpredetermined fidelity, entanglement and/or coherence properties. Thefidelity system can tag a bad qubit to inform a user that it is bad. Itshould be understood that the fidelity system 326, as well as theassociated configuration of the quantum cache 300, can be configured tooperate with populations of qubits, and not necessarily at a singlequbit-by-qubit level in a deterministic way. That is, groups of qubitsrepresenting a single qubit state are anticipated, and qubit states arerepresented by measurements on the ensemble. In these systems,predetermined fidelity levels would be expected to be based onensembles. Fidelities, entanglement and/or coherence properties can benon-deterministic and represented by probabilities and/or otherstatistical metrics.

Quantum purification techniques can be applied to these ensembles by thefidelity system 326. Generally, the fidelity system is responsible formaintaining qubits or qubit ensembles in the store at a known goodfidelity level for the subsequent provision of that qubit state to anapplication 312, and also for updating, as needed, the associatedclassical data of that qubit with information regarding the fidelity.The fidelity system 326 can remove bad qubits from the store eitherphysically or prevent bad qubits from being unloaded and/or subsequentlyused based on associated classical data information.

In some embodiments, the qubit unloader 316 is connected to anapplication 328. The application may include a quantum measurementsystem (not shown). In these embodiments, the quantum measurement systemdetermines a state of the qubit in the qubit unloader, and this statevalue is used by the application. For example, the state value may bethe same as a state value determined by a measurement of another qubitin a remote cache with which the qubit in the qubit unloader isentangled.

In some embodiments, the application 328 includes a quantum processorsystem (not shown) that uses the stored quantum state information. Thequantum processor can include various quantum logic elements thatperform unitary and/or non-unitary transformations on the quantum state.For example, CNOT, Hadamard and/or Pauli-Z/or Pauli-X/or Pauli-X andPauli-Z and/or measurements can be performed by the application 328.

In some embodiments of the system and method of the present teaching,the qubit unloader 310 and the data unloader 324 are connected to anoptional communications channel 330 via the application 328. The channel330 can support one or both of quantum communication or classicalcommunication via separate or combined channels. The channel 330 allowsthe application 328 to connect separate quantum entangled caches 300together to share either the quantum information or the classicalinformation. The channel 330 can be used to exchange qubits directlyfrom the qubit unloader in one or the other separate quantum entangledcache and/or qubits that are processed by quantum logic elements thatare connected to both the channel and to the qubit unloader 324 in oneor the other quantum cache.

FIG. 4 illustrates an embodiment of a table 400 showing a cachestructure for a quantum entangled cache according to the presentteaching. The cache structure shown in the table 400 includes fields forboth classical information and quantum information. For example, anindex field and an age field are provided. The index associatesparticular items of classical data (e.g. various meta data) withparticular ones of the plurality of quantum states. There is also afield for describing which nodes hold the qubit that the qubit isentangled with. There can be fields for other parameters, for example,type of qubit, half-life of qubit, qubit error rate, qubit access time,and other parameters. Fidelity information can be included. Theclassical information is tagged, in other words indexed, to a particularqubit that resides in the cache, and is also maintained and updated, asneeded, as the qubit is stored in the cache.

Another feature of the systems and methods of the present teaching isthat it accommodates the fact that qubits generated by differentphysical manifestation have different properties and offer differentparameters that can be part of the classical information. For example,some physical qubits can be stored for long time, some physical qubitspreserve entanglement longer than others, some physical qubits are easyto access and use, and other physical qubits require more complex andtime-consuming access schemes. These different physical qubitmanifestations can have different associated classical information thatis appropriate to the physics of those particular qubit manifestations.The qualities of the different physical qubits can influence the designof a cache. As one example, some embodiments of quantum entangled cachesaccording to the present teaching use layered cache systems.

FIG. 5A illustrates a diagram an embodiment of a multilayer quantumstore 500 according to the present teaching. The multilayer quantumstore 500 has a top layer 502 and a bottom layer 504. In this example,the top layer 502 represents a relatively fast-access time, butrelatively low storage time store system, where the bottom layer 504represents a relatively slow access time, but relatively longer termstorage system. In some embodiments, the top layer 502 can be a fiberoptic loop buffer storage system that holds photon qubits. These photonqubits can be single photon qubits, frequency entangled photonic qubits,or they may be polarization encoded qubits. In some embodiments, thebottom layer 504 is an atomic qubit storage system. This bottom layer504 can include any of a variety of known atomic qubits. The top layer502 is used first. This is because the top layer 502 provides lowlatency access to qubits, albeit with qubits that preserve entanglementfor less time. The bottom layer 504 is used for cases where the systemcan support a higher latency access. In some embodiments according tothe present teaching, the bottom layer transfers qubits to the top layerwhen time allows, optimizing the tradeoff between latency andentanglement half-life for a particular application. Bottom layer qubitspreserve entanglement for longer periods of time. For example, photonicqubits are generally difficult to hold for long periods of time, butsimple to access, and so are accessed with lower latency. Atomic qubitscan maintain an entangled state for longer time periods; but have ahigher latency for access. Photons are also generally a plentifulresource, while atomic qubits are less abundant. The multilayer quantumstore 500 of the present teaching appropriately manages and allocatesthe physical qubits based on their individual characteristics. Thus, onekey benefit of quantum caches of the present teaching is that theyprovide a mechanism that allows classical systems to effectively utilizethe quantum states and/or quantum properties from different quantumphysical systems with a common interface and/or representation.

Various known fiber buffers can be used to short-term store, delay orbuffer, photons that carry quantum states. For example, fiber loopbuffers, various optical cavities such as fiber Bragg cavities, slowlight systems. Various nonlinear (for example, four-wave mixing) schemescan be used to produce various short, long and/or controllable delay ofa quantum photon(s) passing through the fiber. Importantly, for systemsand methods of the present teaching, various known attributes (activeand passive) of the fiber buffer produce predetermined delay propertiesof the buffer, and therefore are amenable to being part of the classicalinformation to be tagged with one or more of the photons that are inputto the buffer.

Fiber optic buffers are particularly appropriate as the top layer 502 ofthe quantum storage system. As one example, in some embodiments of thepresent teaching, the top layer 502 of the physical storage systemcomprise a fiber optic buffer that has tunable delay. See, for example,Stéphane Clemmen, Alessandro Farsi, Sven Ramelow, and Alexander L.Gaeta, “All-Optically Tunable Buffer for Single Photons,” Opt. Lett. 43,2138-2141 (2018), which is incorporated herein by reference. One featureof this kind of buffer is that an input pump laser wavelength produces adelay of a quantum-encoded photon. For example, a range of over severalnanoseconds of delay can be deterministically realized by tuning thepump wavelength across a range of wavelengths. Thus, the particular (andvariable) delay information can be included in classical informationassociated with the qubit in these kinds of short term fiber bufferstores. Another feature of this kind of buffer is that a bandwidth ofthe optical photon that is input to the buffer determines the delay. Assuch, classical information associated with the known input spectrum ofthe quantum encoded photon provides information about the realized delayin the short-term store.

In addition to the shorter term stores (for example, fiber opticbuffers), various known atomic and ion-based systems can be used toconstruct quantum stores that store quantum state information accordingto the present teaching. In addition, the quantum information can betransferred from photonic states to the electronic states of atomic andion systems. That is, quantum states carried by photons can be stored inelectronic states in various ions and atoms to realize these longer-termquantum storage systems and also be read out of the systems as photonsand detected. The quantum states stored in atomic and ion-based memoriescan also be read (measure) directly in the electronic domain.

There are numerous known protocols for realizing quantum atomic memoriesincluding, for example, electromagnetic induced transparency (EIT),reversible inhomogeneous broadening (CRIB) and atomic frequency combs(AFC) that can be used for quantum caches of according to the presentteaching. See, for example, Heshami K, England D G, Humphreys P C, etal., “Quantum memories: Emerging Applications and Recent Advances,” JMod Opt. 63, 2005-2028 (2016), which is incorporated herein byreference. While this is expected to change as technology evolves, it isgenerally accepted that losses in optical-fiber-based buffers can limitstorage times to less than a few tens of microseconds. On the otherhand, atomic systems, particularly cold atomic systems can hold quantumstate for times scales on order of seconds or more. These numbers arejust illustrative and not intended to limit the present teaching in anyway, but they serve to illustrate the need for different layers of cacheto support a wide range of storage and access times.

Atomic memories are particularly appropriate as the bottom layer 504 ofthe quantum storage system as they generally exhibit longer storagetimes. As one example, in some embodiments of the present teaching, thebottom layer 504 of the physical storage system comprise acold-atom-based optical quantum memory. See, for example, Y.-W. Cho, G.T. Campbell, J. L. Everett, J. Bernu, D. B. Higginbottom, M. T. Cao, J.Geng, N. P. Robins, P. K. Lam, and B. C. Buchler, “Highly EfficientOptical Quantum Memory with Long Coherence Time in Cold Atoms,” Optica3, 100-107 (2016), which is incorporated herein by reference. Onefeature of this kind of memory is it efficiently absorbs photons, andalso has low de-coherence. In these systems, optical quantum states areloaded into a cold atomic gas that is prepared by an applied magneticfield gradient so spectral components are encoded across the gradient. Acontrolled reversal of the applied magnetic field generates a photonecho from the gas that represents the quantum state of the input opticalphoton. In these systems, the storage time is a function of the inputcontrol pulse duration. The ability to cool the gas affects thede-coherence time. Thus, known and controllable parameters of the memoryimplementation (for example, optical control powers and opticalbandwidths, applied magnetic fields, readout pulse energy bandwidths,etc.) are directly related to the memory quantum performance metrics,such as storage time, readout time, de-coherence, etc. Regardless of theparticular atomic memory protocol, it is thus possible to tag storedquantum states with associated classical information that allows controlof a quantum cache system independent of a particular physicalimplementation of the memory.

It should be understood that the quantum store physical systemsdescribed herein are only some possible specific examples of quantumstores that could be used in the methods and apparatus of the presentteaching. Various known quantum optical buffering and memory schemeshave particular classical information associated with the properties ofthe stored qubit based on the particular properties and protocols of thephysical store system. For example, operating parameters, such as delay,memory depth, storage time, loading latency and/or unloading latency canbe tagged. In addition, various impairments, such as various losses,de-coherence mechanisms, dephasing effects, added background and variousother nonlinear impairments that affect the quantum state can also betagged. In addition, as systems and methods for physical quantum storagemature, the kinds of classical information will change and grow. Afeature of the methods and apparatus of the present teaching is the useof an abstraction layer that accommodates the anticipated changes andmaturation of the underlying physical systems. Thus, embodiments of themulti-layer quantum store 500 can work not only with some of the examplephysical systems provided herein, but other known and future physicalquantum store systems as they emerge. In other words, the presentteachings are not limited by specific types of quantum store systems.

FIG. 5B illustrates an embodiment of a cache 550 that includes aphysical structure with metadata for a multi-layer quantum entangledcache according to the present teaching. The cache 550 includes bothsoftware/information and hardware. There is a quantum element 552 and aclassical element 554. A fidelity system includes a quantum coherenceengine 556 that is connected to the physical qubits in a long-termquantum store 558, and a short-term quantum store 560. The physicalqubits in the long-term quantum store 558 can be, for example, atomicqubits in an atomic memory. The physical qubits in the long-term quantumstore 558 can be electromagnetically-induced-transparency atomic quantummemories. The physical qubits in the long-term quantum store 558 can beany of various other kinds of known long-term quantum memories. Invarious embodiments of the methods and apparatus of the presentteaching, the long-term memories have a half-life that is nominally tensof microseconds, milliseconds, seconds, or tens of seconds. The physicalqubits in the short-term quantum store 560 can be, for example, photonicqubits in a fiber loop memory. The physical qubits in the short-termquantum store 560 can be single-nitrogen-vacancy-center quantummemories. The physical qubits in the short-term quantum store 560 can beany of various other kinds of known short-term quantum memories. Also,in various embodiments of the methods and apparatus of the presentteaching, the short-term memories have a half-life that is nominallynano-seconds to microseconds. Other important factors for the choice ofa quantum memory system include, for example, the read-out mechanism,the quantum fidelity, the storage efficiency, the time-bandwidthproduct, stability and noise as just some specific examples.

The quantum coherence engine 556 uses purification, or some othernon-measurement monitoring technique, to inspect qubits in the short-and long-term store 558, 560 to interrogate their coherence level. Thisall takes place on the quantum side 552 of the cache. When the coherenceengine 556 decides qubits are bad, it then sends over a classicalchannel notification to all other caches of entangled qubits so thosenodes do not use those qubits. The cache 550 uses the entanglement mapinformation 562 in the classical part 554 of the cache 550 to determinewhich nodes must be notified of qubits that are timed-out.

In some embodiments, when a qubit is retired because it has exceeded itslifetime, the whole cache pops up like a stack in a processor. Thequbits on top are the oldest, and most likely to go bad, but ifsomething in the middle of the cache times-out or is determined to benot coherent or entangled, the one below it moves (pops) up one step.When a qubit is pulled from a cache and measured as part of anyalgorithms, that qubit becomes stale. All other node caches need to knowthis information as well. Each cache may determine this information ontheir own by, for example, by independently measuring lifetime, or, insome embodiments caches can be provided this information, like in thecase of an expired or timed-out qubit, a classical channel communicationprotocol process is used for this notification. In a stack model, youjust need to keep synchronized with index numbers in an index column 564because you know qubits are moving along toward the top of the stack.

In some embodiments, once qubits reach a predetermined age threshold, T,the probability they are out of coherence is relatively high. Aclassical age timer keeps track of this time and can automaticallyremove aged-out qubits. The value of T is retained for each qubit in anage timer 566 column of the cache to be associated with each qubit orgroups of the same type of qubit. This is in the classical part 554 ofthe cache 550. There may be two physical age timers, for example, onefor the long cache and one for the short cache. This is useful is somesystems because the long atomic cache might have a longer half-life. Theadvantage to using the age timer is that if all nodes agree on a timingparameter, then messages are not necessary, and classical communicationis not required to indicate if a qubit went bad (lost is quantum stateinformation). In these particular examples, all nodes are synchronizedand will remove aged-out qubits at the same and/or appropriate times.

In some embodiments of methods and apparatus according to the presentteaching, everything stays in the long-term store 558 until it gets nearthe top of the stack. Then the qubits get transferred to the short-termstore 560 so that they are available for immediate use. Then, if qubitsremain in short-term store 560 for too long, the age timer goes off andthey are discarded and a classical message is sent to inform the othernodes to shift up the appropriate stacks.

Another feature of the quantum caches of the present teaching is thatthey can be used in connection with numerous networked applications.Referring back to FIG. 3, numerous applications 328 that run acrossmultiple nodes in a network (of various kinds) can receive qubits forapplication 312 and/or associated classical data for application 325from the quantum store 308 and/or the classical store 322 in each node.Some example multiple-node applications are described below.

FIG. 6A illustrates an embodiment of a bus network 600 using anentangled cache according to the present teaching. A bus network 600 isjust one particular example. It should be understood that other networkarchitectures can be implemented. A number, n, of nodes 602, 602′, 602″are connected to a classical channel 604. Each node 602, 602′, 602″ hasan entangled qubit cache. The caches are supplied by an entanglementserver (not shown). The qubits are organized pairwise between each setof nodes. Thus, node 1 602 has a “column” of qubits that are entangledwith node n 602″, and node 1 602 has another “column” of qubitsentangled with node 2 602′, and so on for each node.

The use of quantum cache for addressing is described in connection withan Ethernet-like protocol. However, it should be understood thatnetworks using entangled cache addressing according to the presentteaching are not so limited. In the particular example described inconnection with FIG. 6, node 1 602 wants to send a packet to node n602″. Node 1 602 broadcasts the packet, which contains an address fieldon the classical Ethernet channel 604. To determine the contents of theaddress field, Node 1 samples M qubits from the node n column in itscache and generates a resulting number that is random. Node n 602″ hasentangled pairs for each of these M qubits in its cache. Node 1 602sends the results of the sampling on the classical Ethernet. Node n 602″samples the entangled pairs from its cache and generates a resultingrandom number, which will match the random address field from Node 1.Node n 602″ matches the random number received on the classical channelto know that the packet is intended for node n.

All other nodes, such as node 2 602′, also sample their qubit cache forM qubits in the column for node 1 602 to see if the packet is addressedto them. Node 2 602′ does not get a match on the random number providedby node 1 602 and received via the classical channel. As such, themeasured random number represents a quantum source-destination pairaddress. The probability of a match being a false match is 1/E, where Eis an error rate described further below.

FIG. 6B illustrates a table 650 showing a structure of an entangledqubit cache for a multi-node network of the present teaching. In table650, N is the size of the address space which requires sqrt(N) bits,I=N+E, where 1/E is the acceptable error probability (rate) whichrequires sqrt(E) bits. The total qubits required=sqrt(I) for the totaladdress space at a given error rate.

The operation of the entangled quantum caches in the nodes 602, 602′,602″ described in connection with FIG. 6A-B is based on an addressingapplication, but numerous other applications can utilize the sharedentanglement in a network configuration according to the presentteaching. Additional application examples are provided herein.

FIG. 7 illustrates a block diagram of an embodiment of a quantum-enabledinformation system 700 that uses an entangled quantum cache 702according to the present teaching. The quantum cache 702 is suppliedentangled qubits from an entanglement server 704 via a quantum portionof a communication channel 706. The quantum cache 702 supplies orderedand tagged entangled qubits to an application 708. The quantum cache 702can also supply associated classical information about the particularassociated ordered tagged qubit to the application 708. The quantumcache 702 is controlled by a processor 710. The processor 710 controls afidelity system 712, a qubit loader 714, and a classical data loader 716in the quantum cache 702. The processor 710 also controls a classicalstore 718 and a quantum store 720 in the quantum cache 702. Theprocessor 710 is in communication with the application 708, so that itcan command the quantum unloader 722 and the classical unloader 724 tosupply entangled qubits and associated classical data to the application708 at a desired time. The desired time may be chosen to ensure thatentangled qubits supplied at two different nodes share an entanglestate, allowing two remote nodes to share correlated state information.The desired time can be on-demand. The desired time can bepredetermined. The desired time can be based on a lifetime of a quantumstate. The desired time can be based on a time when the quantum statewas generated. The desired time can be based on an application demand.For example, an application in various embodiments can access aparticular shared entangled state. Also, for example, an application invarious embodiments can access a particular type of quantum state. Also,for example, an application in various embodiments can access aparticular basis of a quantum state. Also, for example, an applicationin various embodiments can access a particular fidelity of a quantumstate. Also, for example, in various embodiments, an application canaccess a quantum state based on at least one of an entanglementproperty, a basis of a quantum state, a fidelity of a quantum state, atime-of-arrival of a quantum state, a source of a quantum state, an ageof a quantum state, a half-life of a quantum state, a birth time of aquantum state, a time-of-flight of a quantum state, and/or a type of aquantum state.

FIG. 8 illustrates a block diagram of an embodiment of an applicationsystem 800 that utilizes an entangled quantum cache 802 interacting withan application 804 according to the present teaching. A processor 806sends and receives application commands to an application 804. Theprocessor 806 sends quantum cache management commands to a quantum store808. The processor 806 also sends classical cache management commands toa classical store 804.

Some embodiments of the present teaching utilize an abstraction layerthat supports an easy to use an interface for application coders. Thisis referred to as a classical application interface (CAPI). Theabstraction layer translates between a CAPI and a quantum system. Theabstraction layer uses, interprets, and/or generates at least some ofthe classical data associated with a quantum state.

The quantum mechanical nature of quantum devices adds another level ofcomplexity to the underlying behavior of the devices that provide usefulquantum functionality for information system engineering. Most engineersand scientists are trained in basic programming of causal Newtoniansystems. For reference, there are about 1600 quantum physicistsworldwide, yet there are upwards of 20 million software professionalsworldwide. For quantum mechanical systems to be widely adopted, theymust be easily used by classically trained software professionals. Aclassical application interface translates between these worlds. Theadvantage of the CAPI is to allow any coder to apply a quantum system asa black box. It is not necessary for the coder to know how quantumsystems work, only how the quantum systems perform. The CAPI appears toa software developer as a familiar function structure in their chosenprogramming language. The following are some examples to illustrate aCAPI and how it works in an entangled quantum cache that is interfacedto an application. These examples are illustrative and notcomprehensive.

A cache_pointer identifies a particular quantum cache 808, allowing formultiple caches in a single node. Only one node is shown in FIG. 8, butit is understood that the present teaching applies to any number ofnodes. A qubit_pointer identifies a particular qubit in a cache and itsassociated metadata. A node identifies a particular node. A channel (notshown) allows for multiple connections from a single node.

Cache Management Functions include: 1)Integer=Get_Qubit_Count(cache_pointer), that indicates how many qubitsare in cache; 2) Integer=Get_Long_Term_Qubit_count(cache_pointer), thatindicates how many qubits are long term qubits; 3)Integer=Get_Short_Term_Qubit_count(cache_pointer) that indicates howmany qubits are short term qubits; 4)Random_Integer=Sample_Qubit(cache_pointer,qubit_pointer), that indicatessample/collapse to classical; 5)Time=Get_Qubit_Age(cache_pointer,qubit_pointer), that indicates the ageof the qubit; 6) Array(n)=Get_Qubit_Entanglement_Map(cache_pointer,qubit_pointer), that indicates what qubits are entangled; and 7)Local_cache_pointer=Put_Entangled_Qubit(cache_pointer,qubit_pointer,node), that put an entangled qubit over on another node.This function puts one member of an entangled pair at another node. Itshould be understood that the specific calls associated with the cachemanagement functions are presented for illustrative purposes and notintended to limit the present teaching in any way.

In general, an application system 800 that utilizes an entangled quantumcache 802 interacting with an application 804 will include a processor806 that is able to send and receive application commands to anapplication 804 that is easy to use for classically trained softwareengineers and software developers. The abstraction layer limits, forexample, the amount of detailed information needed to control thequantum store 808 and classical store 810 that is passed to theapplication commands generated by the application 804 as illustrated inthe example provided herein.

In one particular example, the application 804 is a quantum privateaddress application that is described in more detail in connection withthe description for FIG. 9. In these embodiments, the applicationcommands include Secret_Address=Get_Address(node_X), that indicates whatis the classical private address that looks random to other nodes.

In other specific embodiments, the application 804 is a super densecoding application that is described in more detail in connection withthe description for FIGS. 10-12, below. In these embodiments, theapplication commands include: 1) Send(transmit_data,channel_number),that indicates send; 2) Receive_Data=received(channel_number,node), thatindicates receive; 3) Integer=Get_Entangled_Count(node_address), thatindicates check cache depth; 4)Allocate_Quantum_Channel(percent,channel_number), that allocates percentof channel for sending qubits.

An embodiment of a classical application interface for a super-densecoding application would include the following commands. For thetransmitter: 1) Establish_Link(5,10), that commands entangled qubits tobe shared between the transmitter and receiver; and 2)Send(“Hello”,5,10), that commands “Hello” to be sent. For the receiverthe commands include: “Hello”=received(5,10), that indicates a “Hello”received. For the processor, the commands include: 1)107=Get_Entangled_Count(10), that indicates we have only 107 entangledqubits left so need to allocate more of the channel to exchangeentangled qubits; 2) Allocate_Quantum_Channel(50,10), that allocates 50%of the channel to build the entangled cache; 3)1025=Get_Entangled_Count(10), that indicates that we now have 1025qubits; and 4) Allocate_Quantum_Channel(5,10), that commands to reduceallocation to 5%.

One feature of the entangled quantum caches of the present teaching isthat they can support a variety of classical, semi-classical, and purequantum applications. Several example applications are provided below.

One application supported by the quantum entangled cache of the presentteaching is providing shared-node metadata for distributed informationsystems. In this application, the qubits in the entangled qubit cachesprovide metadata for one or more of a variety of different classicaldistributed information systems. The shared-node metadata provided bythe quantum entangled caches of the present teaching can support avariety of protocols that can provide, for example, addressing, timing,location and other information being shared between pairs and/or groupsof nodes.

FIG. 9 illustrates an embodiment of a distributed system 900 using anentangled cache to provide shared-node metadata of the present teaching.A communication channel 902 connects a plurality of nodes 904, 906, 908,910. The communication channel 902 supports both quantum communicationand classical communication through any of a variety of means. In thisembodiment, pairs of M entangled qubits are stored in caches in thevarious nodes. For example, as illustrated by the diagram 912, node A904 and B 906 share M entangled qubits. As illustrated by the diagram914, node A 904 and X 908 share M entangled qubits. As illustrated bythe diagram 916, node X 908 and Z 910 share M entangled qubits. Thesevarious sets of M pairs of qubits are appropriately tagged and stored ina cache (not shown) in each node 904, 906, 908, 910, such that they canbe accessed by processors in the nodes 904, 906, 908, 910 for processingand/or measurement to implement a desired protocol. The various Mentangled qubits may be distributed by an entanglement server (notshown) over the communication channel 902, or by different means. Someprotocols will exchange raw or processed qubits from the cache over acommunication channel 902, but other protocols will not require anyexchange of qubits to function.

A packet 918 includes a quantum address and data. The quantum addressis, in some embodiments, a random number that is generated by a sendernode, and received by a potential receiver node. The random numberrepresents a quantum source-destination pair address. A receiver nodemeasures qubits entangled with particular nodes to generate a randomnumber representing source-destination address pairs for thoseparticular nodes. For example, qubits entangled with node A are measuredby a node to determine if a received packet is from node A. If a randomnumber in the quantum address of a packet 918 is a match with a randomnumber generated by a measurement of entangled qubits in a particularreceiving node, then the data in the packet is for that receiving node.

An example of a metadata exchange between node A 904 and node B906 isfollows. Node A 904 measures each of M qubits known to be entangled withnode B and generates a random number that represents an address. Thisrandom number is sent classically in the quantum address field of apacket 918 along with some data. Node B 906 measures each of M qubitsknown to be entangled with node A 904 to generate a random number. NodeB 906 receives the packet 918, and compares the received random numberwith the generated random number. If there is a match, the data is fornode B 906 from node A 904.

Another feature of the present teaching is that the quantum metadataproduced with methods and apparatus according to the present teachingcan be used to prevent anyone from knowing which source-destination pairof nodes is addressed with a quantum key distribution level ofassurance. This is because the quantum entangled caches enable two ormore nodes to share a random number “secret” without any exchange ofclassical data.

In general, such a feature can be applied to any of a variety addressingschemes. For example, addresses can be one or more of network addresses,memory locations, data base indexes, geographical addresses, telephonenumbers, and many other identifiers. Any entity that desires to placedata at, or communicate with, any other entity possesses a number, n,entangled qubits with associated other-paired entangled qubits that arepossessed by the other entity. The number n is typically chosen suchthat it is large enough to minimize address collisions.

One example addressing scheme according to the present teaching is theapplication of the quantum metadata to a quantum Ethernet (broadcastchannel) where the addresses are entangled qubits as described inconnection with FIG. 9. In this addressing scheme, if node A 904 has apacket for node B 906, node 904 encodes using N-qubits in superpositionthat are ordered and entangled with qubits in node B 906. The packetincludes a quantum address from node A 904 and data. Everyone receivesthe packet. Until measurement, none of the nodes 904, 906, 908, 910 knowtheir particular address. When nodes make a measurement, they generate arandom number. Then, node A 904 sends the random number via classicalbroadcast to all the nodes 906, 908, 910. If the random number agreeswith a random number generated in a node when a measurement is made, thepacket is for that node. Thus, the random number represents a quantumsource-destination pair address.

A feature of this method is that an eavesdropper cannot determine whichnode the data was directed to nor can the eavesdropper determine thenode that transmitted the data. The random number broadcast classicallydoesn't reveal anything except to the source and destination pairsharing the data. If the quantum entangled pairs are manipulated by a3^(rd) party, which is measured and/or spoofed, these measurementsand/or spoofing actions are detectable using a quantum key distributionprotocol between the entanglement server and the caches. Said anotherway, if someone tried to determine the source destination pair, or spoofthe source and/or the destination, that action would destroy thecorrelation of the random number. This feature makes the addressingscheme absolutely private to spoofing, which is highly desirable formany applications.

As another example of address according to the present teaching,consider a simple three node network that includes a transmitter and tworeceivers. For example, this three node network includes nodes A 904, B906, and node X 908 of FIG. 9. Rather than being deterministic as inprior art classical addressing schemes, addressing schemes according tothe present teaching are similar to hash collisions. However, a node canmake the probability that data is sent to the wrong entity very small ifthe number of qubits, M, in a cache is much bigger than the addressspace. For the three-node network, with only one entangled qubit pernode, the qubit could end up to be measured as a zero or a one with 50%probability. With five qubits to handle two addresses, the chances thatall three nodes would get the same random number are very small, (½)⁵.To get an address error rate of say ( 1/10)⁷ then 20+n qubits areneeded, where n represents the address space being covered. Usingtwenty-one qubits results in an error rate of (2,000,000)⁻¹, andtwenty-two qubits results in an error rate of (4,000,000)⁻¹, and so on.As such, the number of qubits used per address can be notably largerthan a number of classical address bits.

Generally, the quantum entangled cache system and method of the presentteaching allows nodes to share entangled qubits amongst any other nodeto which they need to communicate. In various embodiments, the data isbroadcast classically, or may also be sent on a quantum channel. Asdescribed above, the entanglement can be N-way entanglement and feedN-caches with M qubits directly from a single server. The entanglementof the M qubits can include K dimensions. Data may be protected usingquantum key exchange and/or encrypted by known classical means. Theaddress information is provided by measuring selected qubits in thequantum entangled caches. A sender makes a measurement and generates arandom number, this number is broadcast with the data. A receiver alsomakes measurement of selected qubits to generate a random number andcompares that number to those received in the addresses of packets onthe network. When the two random numbers match, it can be concluded thatthe data was for that node.

In a network with n nodes participating in such a scheme, every nodeneeds to have paired ensembles of entangled qubits with every othernode. Every transmitter selects one of those paired ensembles to addressa desired node for communication. In some embodiments, each node needs2^((n-1)) pairs of entangled ensembles in order to be able to addressevery other node in network with n nodes. The receiver needs to measureeach of these paired ensembles to do the matching with the transmitter'saddress that's sent classically. And each ensemble needs to have atleast n qubits.

In some embodiments, receivers can do measurements one bit at a time.So, for example, the first bit broadcast is compared to the first qubitin every ensemble. Statistically, this should eliminate ½ the potentialsenders. Then the second qubit, eliminating the next ¼, and so on. Inthis way, the receiver only needs to do n+(n−1)+(n−2)+ . . . =2n(n−1)comparisons. The likelihood that a receiver misidentifies a message notintended for the receiver is ½^(n). As the address space increases, theprobability of misidentified messaged decreases. Error rates inaddressing can be further reduced by increasing the address space, thatis making a more-sparse address space. For example, using an addressspace say 2^(n) for 2^(m) nodes, where n>m, every extra bit ofaddressing reduces the error rate by ½.

One feature of the present teaching is that the receiver actuallyobtains two pieces of information by executing the protocol. First, thereceiver knows that the message was intended for that particularreceive. Second, the receiver knows the address of the source of theinformation.

Some systems according to the present teaching can be used for networkinitialization in the following way. The scheme is used to develop a setof classical addresses, which are the broadcast results of themeasurement. These classical addresses appear to be random numbers toeveryone except the intended receiver. So the transmitter sends aclassical packet with an address header that is truly a random numberdetermined by this scheme. The receiver learns to use classic logic tolook for that number, which is actually the equivalent of a source anddestination address, but looks random to everyone else.

Another feature of the present teaching is that it is possible to tradesecurity for addressing overhead. In some embodiments of the presentteaching, nodes decide how often to refresh the address (reinitialize)based on security needs. To be very secure, the address is refreshed forevery packet. Less secure implementations only do refreshing at chosenintervals, much like updating a password.

Also, some systems according to the present teaching use addressingsystem that uses a quantum entangled cache described herein thatprovides privacy by starting with a shared secret. Every node pair, alsoreferred to as a source-destination pair, shares a secret atinitialization. That secret is an M-bit number, where M-bits is the sizeof the address space. It is important to note that this is for pairs ofnodes, not singular nodes. The M-bit number must exist for every pairthat wants to have a private source destination address. Referring againto the distributed system 900 using an entangled cache of FIG. 9, whennode A 904 wants to talk with node B 906, node A 904 measures M qubitsthat are entangled with M qubits in node B's 906 cache. Node B 906 alsomeasures M qubits that are entangled with M qubits in node A 904.

Then node A 904 does a bit-by-bit classical exclusive (XOR) of the valueof the measured qubits with the shared secret, and sends the result ofthe XOR-ed sample classically over the channel 902 to node B 906. Onlynode B 906 has the shared pairwise secret. Node B 906 does the same XORoperation on the value of the measured qubits, therefore it's lookingfor the same number which still appears to be random. The other nodes,such as node X 908, for example, doesn't have the pair-wise secret, socannot do anything with the quantum address. If node X 908 or other nodesomehow was able to capture the entangled bits destined for node B 906,they are not able to fake the identity of node A 904, because they lackthe shared secret to perform the XOR.

In some methods according to the present teaching, the key is refreshedto prevent having a static key (or secret) using quantum secret tumblingin the following way. At any time, a node pair (node A 904 and node B906, for example) can go into their respective entangled caches andsample (i.e. perform a measurement on M qubits in the cache) again. Insome embodiments, this process occurs after every message. Thatmeasurement result (sample) can be XORed with the original secret. Theresult can become the new, or tumbled, secret that can be used forsubsequent messages. This new, or tumbled, secret can also be referredto as a quantum signature and is one aspect of the present teaching.

Another application of quantum entangled cache systems according to thepresent teaching is the implementation of quantum super dense coding.Super dense coding is a powerful quantum communication scheme thatallows a factor of two increase in the transmission capacity comparedwith a classical communication channel. This is because two classicalbits of information can be sent using one qubit. Quantum cachesaccording to the present teaching serve as a local resource forimplementing the super dense coding protocol.

FIG. 10 illustrates a known quantum super dense coding schemeapplication 1000 operating between a transmitter 1002 and a receiver1004. Two classical bits of information are sent by a transmitter 1002,which we refer to for simplicity as Alice, to a receiver 1004, which werefer to for simplicity as Bob. These information bits, 00, 01, 10, 11,are coded on one of a pair of entangled qubits that is prepared in aBell state by a qubit source 1006. One entangled qubit is provided bythe source 1006 to the transmitter 1002, and is modulated with one ofthe four classical information bits and then sent to the receiver 1004.The other entangled qubit, which is not modulated, is provided to thereceiver 1004 by the source. By processing the modulated qubit and theother entangled qubit, the receiver 1004 is able to determine which ofthe four information bits was sent by the transmitter 1002. The source1006, transmitter 1002 and receiver 1004 use operators such as quantumCNOT 1008, Hadamard 1010 and/or Pauli-Z/or Pauli-X/or Pauli-X andPauli-Z 1012. The receiver 1004 uses a measurement 1014 on both themodulated qubit from the transmitter 1002, and the other qubit of theentangled pair provided by the source 1006 to decode the classicalinformation.

FIG. 11 illustrates an embodiment of a super-dense coding system 1100using an entangled cache according to the present teaching. Thetransmitter 503 and receiver 505 can operate as described above inconnection with FIG. 5. A cache 1104 is connected to the transmitter503, and another cache 1106 is connected to the receiver 505. The caches1104, 1106 are connected to an entanglement server 1102. In someembodiments, this connection is provided by a quantum link 1108, but itshould be understood that numerous other connection means can also beused. The caches 1104, 1106 are supplied entangled qubit pairs by anentanglement server 1102. The entanglement server fills the caches 1104,1106 with entangled qubits. The caches 1104, 1106 tag the appropriateassociated classical information to each qubit as well as maintainingthe qubit in an entangled state as described herein. In this way, thetransmitter cache 1104 and the receiver cache 1106 are populated.

Each information bit modulated by the transmitter 503 comprises a qubitpulled from the cache. Each information bit decoded in the receiver 505utilizes a received modulated qubit sent over a quantum channel 1110from the transmitter that is processed as described in connection withFIG. 5 using a qubit that is pulled from the cache 1106. The receiveruses the classical information that is tagged to each qubit in the cache1106 to determine which qubit to pull and process with the modulatedqubit.

In some embodiments, the transmitter 503 applies operators to qubits inorder and sends them to the receiver 505 over a quantum channel 1110.These operators are I: 00, X: 01, Z: 10 and XZ: 11. The receiver 505performs CNOT operations on the cached qubits from the cache 1106 inorder with received qubits from the transmitter 503. This operation isfollowed by a Hadamard transform operator which performs a measurementto decode the classical information bit modulated by the transmitter503. Two bits of classical information are provided over the link 1110using only one qubit resource.

FIG. 12 illustrates another embodiment of a super-dense coding system1200 using an entangled cache according to the present teaching. Likethe super-dense coding system 1100 described in connection with FIG. 11,the transmitter 503 and receiver 505 operate as described above inconnection with FIG. 5. In this embodiment, an entanglement server 1202is connected to a transmitter cache 1204 and to a receiver cache 1206but with a different architecture than the super-dense coding system1100 described in connection with FIG. 6. The caches 1204, 1206 aresupplied entangled qubit pairs by entanglement server 1202 and qubitsare tagged to build the caches 1204, 1206. The entanglement server 1202is co-located in one area 1208 with the transmit cache 1204 and thetransmitter 503. A quantum channel 710 connects the transmitting area708 to the receiver 505. The entanglement server 1202 supplies entangledqubits to the receiver cache 706 using the quantum channel 710.

Each information bit modulated by the transmitter 503 includes a qubitpulled from the cache. Each information bit decoded in the receiver 505utilizes a received modulated qubit sent over a quantum channel 1210from the transmitter that is processed as described in connection withFIG. 5 using a qubit that is pulled from the cache 1206. The receiver505 uses the classical information that is tagged to each qubit in thecache 1206 to determine which qubit to pull and process with themodulated qubit. The transmitter 503 applies operators to modulate thequbits from the cache 1204 in order and then sends them to the receiver505 over a quantum channel 610. The receiver 505 performs CNOToperations on the cached qubits from cache 706 in order with receivedqubits from the transmitter 503. The receiver 505 then performs aHadamard operation and performs a measurement to decode the classicalinformation bit modulated by the transmitter 503. The result is that twobits of classical information are provided over the link 1210 using onlyone qubit resource.

In some embodiments, the entanglement server 1202 uses quiet channelintervals to fill the remote cache 1206 at the receiver 505 withentangled qubits. In some embodiments, the transmitter 503 is sendingentangled qubits in advance of knowing what data is desired to betransmit. The transmitter 503 decides what is desired to be sent, andonly sends one qubit for every 2 bits of classical data. The otherclassical “bit” is derived by the receiver 505 using a combination ofthe transmitted qubit and the entangled qubit that may be sent way inadvance. The result is communication with non-causal-like behavior.

It should be understood that the super dense coding systems withentangled caches described in connection with FIGS. 11-12 are just somespecific examples of the systems and methods of the present teaching.Numerous other architectures can be implanted with the teachingsdescribed herein. In various embodiments, various elements of the codingsystems 1100, 1200 may be remotely located or co-located. The distancebetween elements also varies with the specific implementation. Forexample, in numerous embodiments of systems according to the presentteaching, all or some of the elements can be located on a samebackplane, card, box, rack, or room. Also, in numerous embodiments ofsystems according to the present teaching, all or some of the elementscan be located across a variety of geographical regions from close tofar distances, including both terrestrial and space-based locations.Connection channels can be implemented in a variety of photonic and/orelectronic means, including wireless and wired channels.

While the examples of quantum entangled caches described herein arehighly simplified, the caches can include qubits from numerousentanglement servers that can be used for various different purposes insupport of different services and processing applications. For example,one or more caches can store one or more types of qubits, includingdifferent types of physical qubits, with different entanglementconditions and entanglement partners. Also, for example, the caches canprovide an application access to a particular quantum state at aparticular time. Also, for example, the caches can provide anapplication access to a quantum state based on particular classical dataassociated with that quantum state and/or at a particular time. Cachescan be architected in various configurations, such as FIFO, LIFO, randomaccess, and combinations of these and other storage architectures.

EQUIVALENTS

While the Applicant's teaching is described in conjunction with variousembodiments, it is not intended that the Applicant's teaching be limitedto such embodiments. On the contrary, the Applicant's teachingencompasses various alternatives, modifications, and equivalents, aswill be appreciated by those of skill in the art, which may be madetherein without departing from the spirit and scope of the teaching.

What is claimed is:
 1. A quantum cache comprising: a) a quantum store having an input that receives a plurality of quantum states having fundamental quantum properties comprising superposition, the quantum store configured to store and order the plurality of quantum states and to provide select ones of the stored and ordered plurality of quantum states to a quantum data output at a first desired time; b) a fidelity system having an input that is coupled to the quantum store, the fidelity system configured to determine fidelity information associated with a coherence property of at least some of the plurality of quantum states and further configured to discard at least some quantum states based on the coherence property; c) a classical store coupled to the fidelity system, the classical store configured to store classical data comprising the determined fidelity information and an index that associates particular ones of classical data with particular ones of the plurality of quantum states and to supply at least some of the classical data to a classical data output at a second desired time; and d) a processor connected to the classical store, the processor determining the first desired time based on the index.
 2. The quantum cache of claim 1 wherein the quantum store is further configured to perform last-in-first-out (LIFO) quantum state ordering.
 3. The quantum cache of claim 1 wherein the quantum store is further configured to provide random access to at least some of the ordered plurality of quantum states to the quantum data output at the first desired time.
 4. The quantum cache of claim 1 further comprising a quantum state loader that provides the plurality of quantum states to the quantum store.
 5. The quantum cache of claim 1 further comprising a quantum state unloader that provides the order plurality of quantum states to the quantum data output at the first desired time.
 6. The quantum cache of claim 1 wherein the fidelity system comprises an age out timer.
 7. The quantum cache of claim 1 wherein the fidelity system is further configured to remove quantum states based on a value of an entanglement property.
 8. The quantum cache of claim 1 wherein the fidelity system is further configured to determine the fidelity of the at least some of the ordered plurality of quantum states in a probabilistic way.
 9. The quantum cache of claim 1 wherein the classical store is configured to store classical data comprising at least one of a time of at least some of the plurality of quantum states, a determined fidelity of at least some of the plurality of quantum states, and a position of at least some of the plurality of quantum states in the ordered plurality of quantum states.
 10. The quantum cache of claim 1 wherein the stored classical data comprises an entanglement map of quantum states in the quantum store.
 11. The quantum cache of claim 1 wherein the processor is further configured to determine the index.
 12. The quantum cache of claim 1 wherein the processor is further configured to determine the first desired time based on the particular ones of classical data associated with the index.
 13. The quantum cache of claim 12 wherein the particular ones of classical data associated with the index comprise at least one of an entanglement property, a basis of a quantum state, a fidelity of a quantum state, a time-of-arrival of a quantum state, a source of a quantum state, an age of a quantum state, a half-life of a quantum state, a birth time of a quantum state, a time-of-flight of a quantum state, or a type of a quantum state.
 14. The quantum cache of claim 1 wherein the fidelity system is further configured to discard quantum states that have collapsed into classical states.
 15. The quantum cache of claim 1 wherein the fidelity system is further configured to determine fidelity information of at least some of the plurality of quantum states in a deterministic way.
 16. The quantum cache of claim 1 wherein the fidelity system is further configured to determine fidelity information of at least some of the plurality of quantum states based on ensembles of quantum states.
 17. The quantum cache of claim 1 wherein the fidelity system is further configured to determine fidelity information of at least some of the plurality of quantum states based on a predetermined half-life of the ordered quantum state.
 18. The quantum cache of claim 1 wherein the fidelity system is further configured to perform quantum purification.
 19. The quantum cache of claim 1 wherein the fidelity system further comprises a quantum coherence engine that is configured to determine a fidelity of at least some of the plurality of quantum states.
 20. The quantum cache of claim 1 wherein the quantum store is configured to maintain fidelity of quantum states to a predetermined level.
 21. The quantum cache of claim 1 wherein the quantum store comprises an atomic memory.
 22. The quantum cache of claim 1 wherein the quantum store comprises an electromagnetically-induced-transparency atomic quantum memory.
 23. The quantum cache of claim 1 wherein the quantum store comprises a fiber buffer.
 24. The quantum cache of claim 1 wherein the quantum store comprises hierarchical fiber loops that provide the ordering of the plurality of quantum states.
 25. The quantum cache of claim 1 wherein the quantum store is further configured to interleave the plurality of quantum states.
 26. The quantum cache of claim 1 wherein the quantum store is further configured to perform first-in-first-out (FIFO) quantum state ordering.
 27. The quantum cache of claim 1 wherein at least one of the plurality of quantum states comprises a qubit.
 28. The quantum cache of claim 27 wherein the qubit comprises a photonic qubit.
 29. The quantum cache of claim 27 wherein the qubit comprises an atomic qubit.
 30. The quantum cache of claim 1 wherein at least one of the plurality of quantum states comprises an entangled photon.
 31. The quantum cache of claim 1 wherein at least one of the plurality of quantum states comprises an entangled atomic spin.
 32. The quantum cache of claim 1 wherein at least one of the plurality of quantum states comprises a quantum state of an ensemble of quantum physical systems.
 33. The quantum cache of claim 1 wherein the quantum store comprises a multilayer quantum store.
 34. The quantum cache of claim 33 wherein the multilayer quantum store comprises at least one fiber optic loop buffer storage system.
 35. The quantum cache of claim 33 wherein the multilayer quantum store comprises at least one atomic qubit storage system.
 36. A method of storing quantum states, the method comprising: a) ordering a plurality of quantum states having fundamental quantum properties comprising superposition; b) storing the ordered plurality of quantum states; c) providing select ones of the ordered plurality of quantum states at a first desired time; d) determining fidelity information associated with a coherence property of at least some of the plurality of ordered quantum states; e) discarding at least some quantum states based on the coherence property; f) storing classical data comprising the determined fidelity information and an index that associates particular ones of classical data with particular ones of the plurality of quantum states; g) providing the classical data at a second desired time; and h) determining the first desired time based on the index.
 37. The method of claim 36 wherein the determining the first desired time based on the index comprises determining the first desired time based on the particular ones of classical data associated with the index.
 38. The method of claim 36 wherein the particular ones of classical data associated with the index comprise at least one of an entanglement property, a basis of a quantum state, a fidelity of a quantum state, a time-of-arrival of a quantum state, a source of a quantum state, an age of a quantum state, a half-life of a quantum state, a birth time of a quantum state, a time-of-flight of a quantum state, or a type of a quantum state.
 39. The method of claim 36 further comprising maintain entanglement of the quantum states to a predetermined level until the select ones of the ordered plurality of quantum states are provided at a first desired time.
 40. The method of claim 36 further comprising interleaving the plurality of quantum states.
 41. The method of claim 36 wherein the ordering of the plurality of quantum states is first-in-first-out (FIFO) ordering.
 42. The method of claim 36 wherein the determining fidelity information associated with the coherence property comprises determining the fidelity information in a deterministic way.
 43. The method of claim 36 wherein the determining fidelity information associated with the coherence property comprises determining the fidelity information in a probabilistic way.
 44. The method of claim 36 wherein the determining fidelity information associated with the coherence property comprises determining the fidelity information based on ensembles of quantum states. 